Detailed example counts for week of 2018-12-03 across
type and direction.
Overview of months, inbound
Frequency of net from whole period
Frequency of stocks from whole period
Detailed example counts for week of 2018-12-09 across
type of data.
Overview of months, connected users
Frequency of counts from whole period
# ####
# Jeffreys prior
a1 <- 5e-5
b1 <- 5e-5
lgprior1 <- list(prec = list(param = c(a1, b1)))
# Gelman prior
a2 <- -0.5
b2 <- 5e-5
lgprior2 <- list(prec = list(param = c(a2, b2)))
# iid prior
# Schrödle & Held 2010 & Blangiardo et al 2013
a0 <- 1
b0 <- 0.1
prior.nu <- list(prec = list(param = c(a0, b0)))
# intercept & fixed
inla.set.control.fixed.default()
# intercept ~ N(0,0)
# other fixed effects ~ N(0, 0.001)
#
# where the format is N(mean, precision)
# precision = inverse of the variance.
# PC prior
U <- 1
hyper.prec = list(theta = list(
prior = "pc.prec",
param = c(U, 0.01)
))
# scaling
inla.setOption(scale.model.default = TRUE)mod1 <- inla(users_mac ~
f(stock, model = "rw1", scale.model = TRUE, hyper = hyper.prec),
family = "nbinomial",
control.compute = list(dic= TRUE, waic = TRUE),
data = data)
Call:
c("inla.core(formula = formula, family = family, contrasts = contrasts,
", " data = data, quantiles = quantiles, E = E, offset = offset, ", "
scale = scale, weights = weights, Ntrials = Ntrials, strata = strata,
", " lp.scale = lp.scale, link.covariates = link.covariates, verbose =
verbose, ", " lincomb = lincomb, selection = selection, control.compute
= control.compute, ", " control.predictor = control.predictor,
control.family = control.family, ", " control.inla = control.inla,
control.fixed = control.fixed, ", " control.mode = control.mode,
control.expert = control.expert, ", " control.hazard = control.hazard,
control.lincomb = control.lincomb, ", " control.update =
control.update, control.lp.scale = control.lp.scale, ", "
control.pardiso = control.pardiso, only.hyperparam = only.hyperparam,
", " inla.call = inla.call, inla.arg = inla.arg, num.threads =
num.threads, ", " blas.num.threads = blas.num.threads, keep = keep,
working.directory = working.directory, ", " silent = silent, inla.mode
= inla.mode, safe = FALSE, debug = debug, ", " .parent.frame =
.parent.frame)")
Time used:
Pre = 0.704, Running = 4.94, Post = 0.535, Total = 6.18
Fixed effects:
mean sd 0.025quant 0.5quant 0.975quant mode kld
(Intercept) 7.416 0.006 7.404 7.416 7.427 7.416 0
Random effects:
Name Model
stock RW1 model
Model hyperparameters:
mean sd 0.025quant
size for the nbinomial observations (1/overdispersion) 6.93 0.136 6.67
Precision for stock 3.36 0.708 2.19
0.5quant 0.975quant mode
size for the nbinomial observations (1/overdispersion) 6.93 7.20 6.93
Precision for stock 3.28 4.96 3.12
Deviance Information Criterion (DIC) ...............: 79444.34
Deviance Information Criterion (DIC, saturated) ....: 153614.32
Effective number of parameters .....................: 121.68
Watanabe-Akaike information criterion (WAIC) ...: 79467.01
Effective number of parameters .................: 138.42
Marginal log-Likelihood: -47532.98
is computed
Posterior summaries for the linear predictor and the fitted values are computed
(Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
mod2 <- inla(users_mac ~
weekday +
f(stock, model = "rw1", scale.model = TRUE, hyper = hyper.prec),
family = "nbinomial",
control.compute = list(dic= TRUE, waic = TRUE),
data = data)
Call:
c("inla.core(formula = formula, family = family, contrasts = contrasts,
", " data = data, quantiles = quantiles, E = E, offset = offset, ", "
scale = scale, weights = weights, Ntrials = Ntrials, strata = strata,
", " lp.scale = lp.scale, link.covariates = link.covariates, verbose =
verbose, ", " lincomb = lincomb, selection = selection, control.compute
= control.compute, ", " control.predictor = control.predictor,
control.family = control.family, ", " control.inla = control.inla,
control.fixed = control.fixed, ", " control.mode = control.mode,
control.expert = control.expert, ", " control.hazard = control.hazard,
control.lincomb = control.lincomb, ", " control.update =
control.update, control.lp.scale = control.lp.scale, ", "
control.pardiso = control.pardiso, only.hyperparam = only.hyperparam,
", " inla.call = inla.call, inla.arg = inla.arg, num.threads =
num.threads, ", " blas.num.threads = blas.num.threads, keep = keep,
working.directory = working.directory, ", " silent = silent, inla.mode
= inla.mode, safe = FALSE, debug = debug, ", " .parent.frame =
.parent.frame)")
Time used:
Pre = 0.603, Running = 6.01, Post = 0.503, Total = 7.12
Fixed effects:
mean sd 0.025quant 0.5quant 0.975quant mode kld
(Intercept) 7.373 0.014 7.345 7.373 7.400 7.373 0
weekdayMonday 0.030 0.020 -0.008 0.030 0.069 0.030 0
weekdaySaturday 0.000 0.021 -0.041 0.000 0.041 0.000 0
weekdaySunday 0.026 0.021 -0.016 0.026 0.068 0.026 0
weekdayThursday 0.232 0.020 0.194 0.232 0.271 0.232 0
weekdayTuesday -0.041 0.020 -0.079 -0.041 -0.002 -0.041 0
weekdayWednesday 0.030 0.020 -0.009 0.030 0.068 0.030 0
Random effects:
Name Model
stock RW1 model
Model hyperparameters:
mean sd 0.025quant
size for the nbinomial observations (1/overdispersion) 7.22 0.140 6.94
Precision for stock 3.95 0.788 2.63
0.5quant 0.975quant mode
size for the nbinomial observations (1/overdispersion) 7.21 7.50 7.21
Precision for stock 3.87 5.71 3.72
Deviance Information Criterion (DIC) ...............: 79219.74
Deviance Information Criterion (DIC, saturated) ....: 153389.73
Effective number of parameters .....................: 120.52
Watanabe-Akaike information criterion (WAIC) ...: 79230.99
Effective number of parameters .................: 127.12
Marginal log-Likelihood: -47456.16
is computed
Posterior summaries for the linear predictor and the fitted values are computed
(Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
mod3 <- inla(users_mac ~
weekend +
weekday +
f(stock, model = "rw1", scale.model = TRUE, hyper = hyper.prec),
family = "nbinomial",
control.compute = list(dic= TRUE, waic = TRUE),
data = data)
Call:
c("inla.core(formula = formula, family = family, contrasts = contrasts,
", " data = data, quantiles = quantiles, E = E, offset = offset, ", "
scale = scale, weights = weights, Ntrials = Ntrials, strata = strata,
", " lp.scale = lp.scale, link.covariates = link.covariates, verbose =
verbose, ", " lincomb = lincomb, selection = selection, control.compute
= control.compute, ", " control.predictor = control.predictor,
control.family = control.family, ", " control.inla = control.inla,
control.fixed = control.fixed, ", " control.mode = control.mode,
control.expert = control.expert, ", " control.hazard = control.hazard,
control.lincomb = control.lincomb, ", " control.update =
control.update, control.lp.scale = control.lp.scale, ", "
control.pardiso = control.pardiso, only.hyperparam = only.hyperparam,
", " inla.call = inla.call, inla.arg = inla.arg, num.threads =
num.threads, ", " blas.num.threads = blas.num.threads, keep = keep,
working.directory = working.directory, ", " silent = silent, inla.mode
= inla.mode, safe = FALSE, debug = debug, ", " .parent.frame =
.parent.frame)")
Time used:
Pre = 0.5, Running = 6.45, Post = 0.288, Total = 7.24
Fixed effects:
mean sd 0.025quant 0.5quant 0.975quant mode kld
(Intercept) 7.373 0.014 7.345 7.373 7.400 7.373 0
weekendWeekend 0.009 18.257 -35.837 0.008 35.824 0.009 0
weekdayMonday 0.030 0.020 -0.008 0.030 0.069 0.030 0
weekdaySaturday -0.009 18.257 -35.854 -0.009 35.807 -0.009 0
weekdaySunday 0.017 18.257 -35.828 0.017 35.833 0.017 0
weekdayThursday 0.232 0.020 0.194 0.232 0.271 0.232 0
weekdayTuesday -0.041 0.020 -0.079 -0.041 -0.002 -0.041 0
weekdayWednesday 0.030 0.020 -0.009 0.030 0.068 0.030 0
Random effects:
Name Model
stock RW1 model
Model hyperparameters:
mean sd 0.025quant
size for the nbinomial observations (1/overdispersion) 7.22 0.141 6.94
Precision for stock 3.93 0.797 2.63
0.5quant 0.975quant mode
size for the nbinomial observations (1/overdispersion) 7.22 7.50 7.21
Precision for stock 3.84 5.76 3.65
Deviance Information Criterion (DIC) ...............: 79219.89
Deviance Information Criterion (DIC, saturated) ....: 153389.87
Effective number of parameters .....................: 120.60
Watanabe-Akaike information criterion (WAIC) ...: 79230.98
Effective number of parameters .................: 127.05
Marginal log-Likelihood: -47456.69
is computed
Posterior summaries for the linear predictor and the fitted values are computed
(Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')